Chapter 6 | Applications of Integration
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Figure 6.60 We first choose a frame of reference.
To find the width function, we again turn to similar triangles as shown in the figure below.
Figure 6.61 We use similar triangles to determine a function for the width of the dam. (a) Assumed dimensions of the dam; (b) highlighting the similar triangles.
From the figure, we see that w ( x ) =750+2 r . Using properties of similar triangles, we get r = 250 − (1/3) x . Thus, w ( x ) =1250− 2 3 x (step 2). Using a weight-density of 62.4 lb/ft 3 (step 3) and applying Equation 6.13 , we get
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